Math basics › Quadratics and polynomials
Completing the square
The move
Take half of b, square it, add and subtract it. x² + 6x becomes x² + 6x + 9 − 9, which is (x + 3)² − 9.
Why bother
It turns any quadratic into vertex form, so the vertex can be read straight off. It is also where the quadratic formula comes from.
If a is not 1
Factor a out of the x² and x terms first, then complete the square inside the bracket.